This invention relates to magnetotelluric geophysical exploration, and more particularly, to plotting magnetotelluric impedances in a manner which makes them more useful.
It has long been known that telluric currents circulate beneath the surface of the earth. The prior art suggests that the measurement of these naturally occurring currents will indicate the resistivity of the earth and hence the geophysical characteristics of the subsurface. These telluric currents are subject to variations caused by external influences, such as sunspot activity. Because these variations are unpredictable, measurement of telluric currents was little used as a geophysical exploration tool until Louis Cagniard devised a mathematical technique capable of accounting for these variations. His work is represented, for example, in U.S. Pat. No. 2,677,801 wherein he proposes measuring not only the telluric currents, but also the magnetic field at a measurement station on the earth's surface. Cagniard teaches that a specific relationship exists between the measured orthogonal components of the earth's magnetic field and the measured orthogonal components of the earth's electric (or "telluric") field, and that spatial variations therein may be used to derive specific information regarding the subterranean structure of the earth. As certain structures are known to be indicative of the presence of minerals, these magnetotelluric measurements are a useful prospecting tool.
The Cagniard method of magnetotelluric exploration usually involves the measurement of signals representing the magnetic field and the electric field in two orthogonal directions, usually denoted by H.sub.x, H.sub.y, E.sub.x and E.sub.y respectively. In this type of exploration it is desirable to record the electric field and the magnetic field at spaced locations along a line of exploration.
"Multiple Site Magnetotelluric Measurements", U.S. Pat. No. 4,286,218 to Bloomquist, Hoehn, Norton and Warner, discloses a method of magnetotelluric exploration in which multiple measurements of the earth's electric field as a function of time are made at spaced locations on the earth's surface. One or more measurements of the earth's magnetic field are made simultaneously and recorded.
The electric and magnetic field measurements in general are related to the impedance components of the earth in the following manner: EQU E.sub.x =Z.sub.xx H.sub.x +Z.sub.xy H.sub.y EQU E.sub.y =Z.sub.yz H.sub.x +Z.sub.yy H.sub.y
This may be expressed by the tensor relationship: ##EQU1## The impedances Z.sub.xx and Z.sub.yy arise because of the coupling of transverse electric and transverse magnetic fields by certain types of resistivity variation. The impedances Z.sub.xy and Z.sub.yx are referred to as the Cagniard impedance components. Analysis of the properties of the impedance tensor shows that it is direction dependent. It is possible to determine the dimensionality of the resistivity variation and this information is extremely useful. It is important to determine the dimensions of resistivity variation, because interpreting a two dimensional variation as one dimensional or a three dimensional variation as two dimensional often leads to large errors in the predicted resistivity values. See Ranganayaki, R. P. and Madden, T. R., 1980, "Generalized Thin Sheet Analysis in Magnetotellurics: An Extension of Price's Analysis," Geophysical J. R. Astr. Soc., Vol. 60, pp. 445-457, and Ting S. C., and Hohmann, G. W., 1981, "Integral Equation Modeling of Three-Dimensional Magnetotelluric Response", Geophysics, Vol. 46, No. 2, pp. 182-197.
The prior art has described a way by which the dimensionality of the resistivity variation can be determined. Amplitude polar diagrams of Z.sub.xy (or Z.sub.yx) and Z.sub.xx (Z.sub.yy) are described in Reddy, I. K., Rankin, D., and Phillips, R. J., 1977, "Three-Dimensional Modeling in Magnetotelluric and Magnetic Variational Sounding", Geophy. J.R. Astr. Soc., Vol. 51, pp. 313-325, and in the aforementioned Ting and Hohmann 1981 articles. For one dimensional variation, the amplitude of Z.sub.xx (Z.sub.yy) is zero and Z.sub.xy (Z.sub.yx) is circular because it has the same magnitude in all directions. For two dimensional variation Z.sub.xy (Z.sub.yx) has a maximum or minimum parallel or perpendicular to the strike and Z.sub.xx (Z.sub.yy) is symmetric about the strike direction. For three dimensional variation the magnitude Z.sub.xx (Z.sub.yy) is no longer symmetric. Either it is assymetric or is a curve that does not go to zero in any direction.
In accordance with the present invention, another method is based on the properties of the impedance tensor as described in Word, D. R., Smith, H. W., and Bostick, F. X. Jr., 1970, "An Investigation of the Magnetotelluric Tensor Impedance Method", EGRL Tech. Rep. No. 82, Univ. of Texas at Austin. Sims, W. E., 1969, "Methods of Magnetotelluric Analysis", Ph.D. Dissertation, The Univ. of Texas--January, 1969, shows that the loci of impedance tensor elements in the complex plane as a function of rotation angle are in general ellipses of the same dimensions and orientations centered at ##EQU2##
Z.sub.1 and Z.sub.2 are invariant under rotation. The shape of the rotation loci depends upon the resistivity variation at the measurement site. If the resistivity variation is three dimensional, the surface impedance loci are ellipses; for two dimensional resistivity variations, the loci reduce to straight lines, i.e., the minor axis of the rotational ellipse goes to zero. If the resistivity variation is one dimensional, the locus reduces to a point in the complex plane, i.e., in this case, even the major axis of the ellipse goes to zero. This is explained in the aforementioned Word, et al. article.
Another problem is interpreting magnetotelluric data is that a resistivity anomaly near the surface affects measurements at greater and greater distances as the frequency decreases. Because of this, a low frequency effect measured at any point could be caused by either a lateral variation in resistivity near the surface or a variation at depth. Phase polar diagrams have been used to reduce this ambiguity and to help in determining the depth of an anomaly. The amplitude polar diagrams discussed above respond mostly to the near surface anomaly and are therefore, not particularly useful in delineating deeper anomalies in the presence of a near surface anomaly. Amplitude polar diagrams, once affected by an anomaly, remain affected for a considerable part of the frequency spectrum.
It is an object of the present invention to plot magnetotelluric measurements in a manner in which the structure and resistivity variation of an anomaly can be easily interpreted.